Future developments of lighter, more compact and powerful motors – driven by environmental and sustainability considerations in the transportation industry – involve higher stresses, currents and electromagnetic fields. Strong couplings between mechanical, thermal and electromagnetic effects will consequently arise and a consistent multiphysics modeling approach is required for the motors’ design. Typical simulations – the bulk of which are presented in the electrical engineering literature – involve a stepwise process, where the resolution of Maxwell’s equations provides the Lorentz and magnetic forces which are subsequently used as the external body forces for the resolution of Newton’s equations of motion.

The work presented here proposes a multiphysics setting for the equations governing electric motors. Using the direct approach of continuum mechanics, a general framework that couples the electromagnetic, thermal and mechanical fields is derived using the basic principles of thermodynamics. Particular attention is paid to the derivation of the coupled constitutive equations for isotropic materials under small strain but arbitrary magnetization.

Due to the complex geometry of a typical electric motor, numerical solutions of the governing equations are in order. To gain insight, the theory is hereby applied to obtain the analytical solution of an idealized asynchronous motor for which we calculate the electric current, magnetic, stress and temperature fields as a function of the applied current and slip parameter. The different components of the stress tensor and body force vector are compared to their purely mechanical counterparts due to inertia, quantifying the significant influence of electromagnetic phenomena.

受运输行业的环境和可持续性考虑驱动，更轻，更紧凑和功能更强大的电动机的未来发展涉及更高的应力，电流和电磁场。因此，将在机械，热和电磁效应之间产生强烈的耦合，并且对于电动机的设计需要一致的多物理场建模方法。典型的仿真（其中大部分在电机工程文献中进行了介绍）涉及一个逐步过程，其中麦克斯韦方程组的分辨率提供了洛伦兹力和磁力，这些力随后被用作体外力来解决牛顿运动方程式。

这里提出的工作为控制电动机的方程式提出了一个多物理场设置。使用连续力学的直接方法，使用热力学的基本原理得出了将电磁场，热场和机械场耦合的通用框架。特别注意在小应变但任意磁化的情况下各向同性材料的耦合本构方程的推导。

由于典型电动机的复杂几何形状，因此控制方程的数值解是有序的。为了获得见识，本文将理论应用到理想化异步电动机的解析解中，根据该解析解，我们可以根据施加的电流和滑差参数来计算电流，磁场，应力和温度场。由于惯性，将应力张量和体力矢量的不同部分与其纯机械部分进行比较，从而量化了电磁现象的重大影响。